Depending upon your reference threat model, total isolation might be a
too hard proposition.
In current computer architectures, we have a number of shared
resources that might be exploited to carry attacks (within threat
model) that successfully violate one or more desirable security goals.
As a case in point, let's suppose you are concerned about cache
attacks and desire to prevent sensitive data processed by the
hypervisor leaking to the host machines. Decoupling the hypervisor CPU
from the host CPU will not allow you to rule out such kind of attack.
In fact, one or more levels of memory in the cache hierarchy for your
target processor might be (or might be not!) shared.
Cheers,
Alfonso